Alligation or Mixture - Aptitude Questions and Answers

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In what ratio should water be mixed with wine that costs Rs. 60 per litre so that after selling the resultant mixture at Rs.50 per litre, the profit will be 25%?

A)
1 : 2

B)
2 : 3

C)
3 : 4

D)
4 : 5


Correct Answer :

1: 2


Explanation :

Let X is the cost of pure wine. Then,
Cost of resultant mixture,
X + 25% of X = 50
100X + 25X = 50*100
125X = 50 *100
X = (50 *100)/125 = (2 *20) =Rs. 40

So, wine of Rs. 40(CP) sold at Rs. 50(SP)

Now, in Rs. 60 = 1 litre wine.
So, in Rs.40 = 40/60 = 2/3 part wine, remaining part 1/3 water.
Therefore ratio water:wine
1/3 : 2/3
= 1:2

In what ratio should water be mixed with wine, that costs Rs.60 per litre, so that the price of the resultant mixture is Rs.40 per litre?

A)
2 : 3

B)
4 : 5

C)
3 : 4

D)
1 : 2


Correct Answer :

1 : 2


Explanation :

By the rule of alligation: If two ingredients are mixed, then
Quantity of cheaper/Quantity of dearer =[(C.P. of dearer) - (Mean price)] / (Mean price) - [(C.P. of cheaper)]

i.e. (Cheaper Quantity):(Dearer quantity)= (d-m):(m-c).

C.P. of cheaper(in paise) ,Water c=0/lit
C.P. of dearer(in paise),Wine d=60/lit
Mean price(in paise) or resultant mixture costs, m= 40/lit

Thus ,(Cheaper Quantity):(Dearer quantity)= (60-40) / (40- 0)
=> 20:40 =>1:2

16 litres of kerosene is mixed with 5 litres of petrol. The price of kerosene is Rs. 12 per litre and price of petrol is Rs. 33 per litre. The average price of the resultant mixture per litre is?

A)
15 rs

B)
17 rs

C)
21 rs

D)
23 rs


Correct Answer :

17 rs


Explanation :

Average price of the resultant mixture= (16×12+5×33) / (16+5)
=357 / 21
=17

There is 10% water in 100 liters mixture of milk and water. How much more water is to be added to the mixture so that the resultant solution contains 25% water?

A)
15 litre

B)
20 litre

C)
10 litre

D)
None of these


Correct Answer :

20 litre


Explanation :

There is 10% water in 100 liters mixture of milk and water. How much more water is to be added to the mixture so that the resultant solution contains 25% water?

Initial Solution = 100
Initial water =10% of 100 = 10

Let x is the water to be added to the mixture so that the new mixture must have 25% water

new Solution = 100+x
water in new Solution = 10+x

10+x = 25% of (100+x)
10+x = (25/100)*(100+x)
10+x = (1/4)*(100+x)
40+4x=100+x
3x = 60
x = 20 L

In what ratio should the wheat that costs Rs.7.50 per kg, be mixed with the wheat that costs Rs.11 per kg so that the resultant mixture costs Rs.8.25 per kg?

A)
8 : 5

B)
9 : 7

C)
11 : 3

D)
10 : 3


Correct Answer :

11 : 3


Explanation :

By the rule of alligation: If two ingredients are mixed, then
Quantity of cheaper/Quantity of dearer =[(C.P. of dearer) - (Mean price)] / (Mean price) - [(C.P. of cheaper)]

i.e. (Cheaper Quantity):(Dearer quantity)= (d-m):(m-c).

C.P. of cheaper(in paise) , c=750
C.P. of dearer(in paise), d=1100
Mean price(in paise) or resultant mixture costs, m= 825

Thus ,(Cheaper Quantity):(Dearer quantity)= (1100-825) / (825- 750)
= (1100-825) / (825- 750)
=275 / 75
=11 / 3

How much water is to be mixed in 20 liters of 20% sugar solution so that the resultant solution contains 8% sugar?

A)
10 liter

B)
20 liter

C)
24 liter

D)
30 liter


Correct Answer :

30 liter


Explanation :

Initial Solution = 20 liters(water+sugar)
Initial sugar=20%
So, Initial Water=80% of 20 = 16

Let x is the water to be added to the mixture so that the new mixture must have ontains 8% sugar i.e. 92% water

Thus,new Solution = 20+x
water in new Solution = 16+x

16+x = 92% of (20+x)
16+x = (92/100)*(20+x)
16+x = (23/25)*(20+x)

400+25x=460+23x
2x = 60
x = 30 L

In 1 litre mixture of sprit and water, 20% is water. How much sprit should be added, so that the proportion of water becomes 5%?

A)
3 litres

B)
4 litres

C)
5 litres

D)
6 litres


Correct Answer :

3 litres

There are two types of mixture of milk and water. In the first mixture, out of 27 ltr, 24 ltr is milk only and in the second mixture, 40 ltr is milk and 5 ltr is water. Which one mixture is better in terms of milk’s strength?

A)
First

B)
Second

C)
Same in both

D)
Data insufficient


Correct Answer :

Same in both

An ore contains 25% of an alloy that has 90% copper. Other than this, in the remaining 75% of the ore, there is no copper. How many kilograms of the ore are needed to obtain 60 kg of pure copper?

A)
250

B)
275

C)
300

D)
266.66


Correct Answer :

266.66


Explanation :

Let there is 100 kg ore.
25% of ore contains 90% copper,which means 25 kg contains; 25*90/100 = 22.5 kg of copper.

22.5 kg copper included in 100 kg of ore.
Then, 1 kg of copper = 25/100 kg ore contains
Hence, 60 kg copper = 100*60/22.5 = 266.66 kg of ore contains

The ratio of two liquids in a mixture is 3 : 5 and that in another mixture is 6:1. In what ratio these two mixtures must be mixed so as to make the ratio of the two liquids 7:3?

A)
44 : 61

B)
44 : 71

C)
44 : 81

D)
44 : 91


Correct Answer :

44 : 91


Explanation :

By the rule of alligation: If two ingredients are mixed, then
Quantity of cheaper/Quantity of dearer =[(C.P. of dearer) - (Mean price)] / (Mean price) - [(C.P. of cheaper)]

i.e. (Cheaper Quantity):(Dearer quantity)= (d-m):(m-c).

ratio of a liquid1 in mixture1, c=3/8
ratio of a liquid1 in mixture2, d=6/7
Mean ratio of a liquid1 or ratio of a liquid1 in resultant mixture, m= 7/10

Thus ,Required ratio = (6/7 - 7/10) / (7/10 - 3/8)
= ((60-49)/70) / ((28-15)/40)
=(11/70) / (13/40)
=(11*40) / (70*13)
=44 / 91

A mixture of 40 litres of milk and water contains 10% water. How much water should be added so that the water is 20% in the new mixture?

A)
4 L

B)
7 L

C)
5 L

D)
8 L


Correct Answer :

5 L


Explanation :

Initial Solution = 40
Initial water =10% of 40 = 4

Let x water be added then the new mixture must have 20% water

Final Solution = 40+x
Final water = 4+x

4+x = 20% of (40+x )
4+x = (20/100)*(40+x )
4+x = (1/5)*(40+x )
20+5x=40+x
4x=20
x = 5
water to be added to the mixture, x = 5

In Jar A, 180 L milk was mix with 36 L water.Some of this mixture was taken out from Jar A and put it in Jar B. If after adding 6 L of water in the mixture, the respective ratio between milk and water in Jar B was 5 : 2 respectively, what was the amount of mixture that was taken out from Jar A?

A)

24


B)

54


C)

30


D)

36



Correct Answer :

36


Explanation :

Ratio of milk and water in jar A = 180 L : 36 L = 5 : 1
Let, x L of mixture taken out from jar A.

So, Quantity of milk taken out from jar A = x*5/6 = 5x/6
and Quantity of water taken out from jar A = x*1/6 = x/6

Now, according to the question,
(5x/6) / (x/6 + 6) = 5/2
(5x/6) / (x + 36)/6 = 5/2
5x / (x + 36) = 5/2
10x = 5x + 180
5x = 180
x = 36
Hence, 36 L of mixture was taken out from Jar A.

25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is the ratio 1 : 2 and the amount of lead and tin in the alloy Y is in the ratio 2 : 3, then what is the ratio of lead to tin in the mixture?

A)
1 : 2

B)
2 : 3

C)
3 : 5

D)
7 : 11


Correct Answer :

7 : 11


Explanation :

Alloy X
Total 25
Ratio 1:2
lead 25* (1/3)=25/3
tin 25* (2/3)=50/3

Alloy Y
Total 125
Ratio 2:3
lead 125* (2/5)=50
tin 125* (3/5)=75

When X and Y are mixed, then
Amount of lead = (25/3) + 50 = 175/3 kg
Amount of tin = (50/3) + 75 = 275/3 kg

Ratio of lead to tin in the mixture = (175/3) / (275/3) = 175 : 275 = 7 : 11

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